Hello Joyce and welcome! Dahlias are native to and grow wild in many parts of Mexico they are also the national flower of Mexico so i would think they would do very well in zone 9. There may be hybrids that have been designed for colder climates, i don't know. But if you find dahlias that haven't been altered genetically too much, they should do well in your climate. I don't know about the lavender dahlia that you describe. Good luck in finding it!